Related papers: Dualities and endomorphisms of pseudo-cones
This paper consists of three parts: (a) exhibit a new gluing result which can dramatically simplify extensions of calibration pairs; (b) observe that every Lawlor cone can support coflat calibrations singular only at the origin; (c) show…
We study Poincar\'e Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincar\'e Duality. As an application, we give new uniform (and essentially formal)…
This paper is about integral zonotopes. It is proven that large zonotopes in a convex cone have a limit shape, meaning that, after suitable scaling, the overwhelming majority of the zonotopes are very close to a fixed convex set. Several…
Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.
Hyperbolic polynomials elegantly encode a rich class of convex cones that includes polyhedral and spectrahedral cones. Hyperbolic polynomials are closed under taking polars and the corresponding cones, the derivative cones, yield…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…
We show that two smoothly bounded, strongly pseudoconvex domains which are diffeomorphic may be smoothly deformed into each other, with all intermediate domains being strongly pseudoconvex. This result relates to Lempert's ideas about…
We study the class of idempotent-generated pseudo-composition algebras, which is a subclass of the family of axial algebras. More specifically, we utilise the group-algebra correspondence, natural to the axial framework in order to study…
We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces,…
We establish new results concerning endomorphisms of a finite chain if the cardinality of the image of such endomorphism is no more than some fixed number k. The semiring of all such endomorphisms can be seen as a k - simplex whose vertices…
For any Wulff shape, its dual Wulff shape is naturally defined. A self-dual Wulff shape is a Wulff shape equaling its dual Wulff shape exactly. In this paper, it is shown that a Wulff shape is self-dual if and only if the spherical convex…
We classify real two-dimensional orbits of conformal subgroups such that the orbits contain two circular arcs through a point. Such surfaces must be toric and admit a M\"obius automorphism group of dimension at least two. Our theorem…
We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally…
We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This…
It is an interesting question whether a given infra-red duality between quantum field theories can be explained in terms of other more elementary dualities. For example recently it has been shown that mirror dualities can be obtained by…
Let M be a closed simply connected 2n-dimensional manifold. The present paper is concerned with the cohomology of classifying spaces of connected groups of homeomorphisms of M.
Illumination complexes are examples of 'flat polyhedral complexes' which arise if several copies of a convex polyhedron (convex body) Q are glued together along some of their common faces (closed convex subsets of their boundaries). A…
In this paper we study the structure of cellular pseudomanifolds (aka abstract polytopes). These are natural combinatorial generalisations of polytopal spheres (i.e., boundary complexes of convex polytopes). This class is closed under…
Two main topics are considered: The characterisation of finite homomorphism dualities for relational structures, and the splitting property of maximal antichains in the homomorphism order.